TY - JOUR T1 - The Boundedness for Generalized Solutions of Quasilinear Elliptic Equations AU - Liang Xiting JO - Journal of Partial Differential Equations VL - 3 SP - 79 EP - 88 PY - 1991 DA - 1991/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5777.html KW - Elliptic equation KW - critical exponent KW - natural growth condition KW - generalized solution KW - boundedness KW - Hölder continuity AB - Under the appropriate conditions on u, the generalized solution of the elliptic equation ∫_G {∇v ⋅ A(x, u, ∇u) + vB(x, u, ∇u)}dx = 0, \quad ∀v ∈ {\WW}¹_p(G) ∩ L_∞(G) for which even the natural growth condition p(1 - 1/p^∗) < ϒ < p is permitted, the local and global boundedness of u are proved.